Kinematics of Rolling — Wheel of a Car What best describes the motion of a car’s wheel (assuming rolling without slipping)?

Introduction / Context:
Rolling without slipping is a fundamental kinematic model in vehicle dynamics. Each wheel simultaneously rotates about its own axis while the wheel’s center translates along the road.

Given Data / Assumptions:

• No slip condition at the contact (ideal rolling).
• Rigid wheel model for kinematics.

Concept / Approach:
For rolling without slipping, the instantaneous velocity of the contact point relative to the ground is zero. The motion can be decomposed into translation of the center of mass plus rotation about the center with angular speed ω such that v_center = ω * r.

Step-by-Step Explanation:

Verification / Alternative check:
Observe tire tread: points above the center move faster than the vehicle speed, while the contact point is instantaneously at rest. This only occurs with combined translation and rotation.

Why Other Options Are Wrong:
Pure translation would imply no wheel spin; pure rotation would imply spinning in place; “neither” is not physical.

Common Pitfalls:
Confusing slip conditions; forgetting the v = ω r condition for ideal rolling.

Final Answer:
Combined translation and rotation (rolling motion).